Hey, so I just watched the Veritasium video “Something Strange Happens When You Trust Quantum Mechanics” (https://www.youtube.com/watch?v=qJZ1Ez28C-A), and it got me thinking.
The video talks about how light takes every possible path and ends up following the one with the least action. Super cool concept. But then, around the 30-minute mark, there’s this wild experiment where a laser is aimed at one side of a mirror, and there’s a diffraction grating placed on the other side. Even though the laser isn’t hitting the grating directly, you still see light coming out from that side. That part really tripped me up.
So here’s my question: Where is the energy for that “other path” coming from?
My gut says energy has to be conserved, so if light is somehow taking a new path via the grating, does that mean the original laser beam is losing energy? Maybe it just gets dimmer?
But then I thought… what if you could make a really clever diffraction setup that always pulls light along some super-efficient path? Could you, in theory, siphon off light energy from a bulb on the other side of the planet without anyone near the bulb noticing?
And if the original beam’s intensity is not lowered, then we would have generated free energy!
So is this really about energy moving along a new path, or are we just bending scattered light in a clever way to make it look like something more mysterious is going on?
I don’t think this fully answers OP’s question, though (at least as I understand it): while a photon’s wave function spreads out everywhere including the diffraction grating and card, what counts for conservation of energy is where the photon is actually observed. So if we manipulate the interference pattern of the wave function to cause a photon to be observed where the probability would normally cancel to zero—and if the probability of observing the photon somewhere remains one—does that accordingly reduce the probability of observing the photon where we would otherwise have expected to see it?
At this point I have to admit that I am out of my depth. We need a real physics major to chime in.